# DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting

arXiv: https://arxiv.org/abs/2306.01984 · HTML: https://mlsanity.com/paper/2306.01984/

## Key facts

- Cited by 109 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 52 of its 79 references that are in the map.
- First posted on arXiv 3 Jun 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 52)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation](https://mlsanity.com/paper/2205.09853/) (2022)
- [Flexible Diffusion Modeling of Long Videos](https://mlsanity.com/paper/2205.11495/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)

## Built on by (most cited first, 30 of 109)

- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Rolling Diffusion Models](https://mlsanity.com/paper/2402.09470/) (2024)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields](https://mlsanity.com/paper/2406.02176/) (2024)
- [Foundation Models for Weather and Climate Data Understanding: A Comprehensive Survey](https://mlsanity.com/paper/2312.03014/) (2023)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Wavelet Diffusion Neural Operator](https://mlsanity.com/paper/2412.04833/) (2024)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [Text2PDE: Latent Diffusion Models for Accessible Physics Simulation](https://mlsanity.com/paper/2410.01153/) (2024)
- [Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks](https://mlsanity.com/paper/2504.02843/) (2025)
- [AI Foundation Models for Weather and Climate: Applications, Design, and Implementation](https://mlsanity.com/paper/2309.10808/) (2023)
- [Probabilistic Emulation of a Global Climate Model with Spherical DYffusion](https://mlsanity.com/paper/2406.14798/) (2024)
- [Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2501.13329/) (2025)
- [Diffusion Dynamics Models with Generative State Estimation for Cloth Manipulation](https://mlsanity.com/paper/2503.11999/) (2025)
- [Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulation](https://mlsanity.com/paper/2507.02608/) (2025)
- [DiffPhyCon: A Generative Approach to Control Complex Physical Systems](https://mlsanity.com/paper/2407.06494/) (2024)
- [Diffusion Model for Planning: A Systematic Literature Review](https://mlsanity.com/paper/2408.10266/) (2024)
- [Deep Learning and Foundation Models for Weather Prediction: A Survey](https://mlsanity.com/paper/2501.06907/) (2025)
- [Geometric Trajectory Diffusion Models](https://mlsanity.com/paper/2410.13027/) (2024)
- [Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics](https://mlsanity.com/paper/2506.20024/) (2025)
- [Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting](https://mlsanity.com/paper/2410.03229/) (2024)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [Binned Spectral Power Loss for Improved Prediction of Chaotic Systems](https://mlsanity.com/paper/2502.00472/) (2025)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [Hierarchical Implicit Neural Emulators](https://mlsanity.com/paper/2506.04528/) (2025)
- [Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics](https://mlsanity.com/paper/2506.06045/) (2025)

## Abstract (arXiv)

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.